Weibull Modulus Calculator
Fit supplied failure-strength Weibull plotting positions, not censored maximum-likelihood reliability or automatic plotting-position policy. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.
Description
A Weibull probability plot relates transformed cumulative probabilities to logarithmic strength.
A Weibull probability plot relates transformed cumulative probabilities to logarithmic strength.1
Its fitted slope describes the supplied plotting data rather than a likelihood fit to raw failures. Use this tool to calculate weibull Modulus from the supplied measurements and assumptions.
When to use Weibull Modulus Calculator
Use this tool to calculate weibull Modulus from the supplied measurements and assumptions. Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
How to use Weibull Modulus Calculator and understand its results
- Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
- Enter orderedFailureStrengthPa, callerPlottingFailureProbabilities, using the field meanings and rules below, then run the tool.
- Read fittedWeibullStrengthModulus, strengthFitRSquared. Interpret the fields using their units, signs and evidence conventions below.
- If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| orderedFailureStrengthPa | Ordered failure strength pa | list of number | Required |
| callerPlottingFailureProbabilities | Caller plotting failure probabilities | list of number | Required |
Enter at least two aligned strictly increasing positive strengths and strictly increasing cumulative probabilities strictly between zero and one. Fit transformed y=ln(−ln(1−probability)) against x=ln(strength) by ordinary least squares and return slope and R². No maximum-likelihood fit, censoring model or plotting-position generation is supplied.
WeibullModulus=OLSslope(lnStrength,ln(−ln(1−probability))) Use the exact units, boundary rules, ordering and missing-evidence conventions above.
| Output field | Meaning | Value type |
|---|---|---|
| fittedWeibullStrengthModulus | Fitted Weibull Strength Modulus; follow the units, sign, ordering and evidence convention stated above | number |
| strengthFitRSquared | Strength Fit R Squared; follow the units, sign, ordering and evidence convention stated above | number |
{
"input": {
"orderedFailureStrengthPa": [
1,
2,
4
],
"callerPlottingFailureProbabilities": [
0.6321205588285577,
0.8646647167633873,
0.9816843611112658
]
},
"output": {
"fittedWeibullStrengthModulus": 0.9999999999999997,
"strengthFitRSquared": 0.9999999999999999
}
}Limitations and assumptions
Its fitted slope describes the supplied plotting data rather than a likelihood fit to raw failures. Interpretation depends on the units, sampling scope and exact model described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.
Alternative or Complementary methods
Use Basquin Fatigue Life Calculator for this related task: Basquin's relation models fatigue life through a calibrated stress-power law.
Use Hall-Petch Strength Calculator when its separate inputs and assumptions fit the question: Hall-Petch strengthening relates a calibrated yield model to inverse square root of grain diameter.
References
-
Weibull Modulus Calculator — tool.io
Similar or alternative tools
- Basquin Fatigue Life Calculator
Basquin's relation models fatigue life through a calibrated stress-power law.
- Hall-Petch Strength Calculator
Hall-Petch strengthening relates a calibrated yield model to inverse square root of grain diameter.